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The statement that "the sum of all natural numbers equals -1/12" is misleading if taken literally. The ordinary series 1 + 2 + 3 + 4 + … diverges, so it does not have a finite sum. The value -1/12 comes from analytic continuation of the Riemann zeta function ζ(s) to s = -1, which is a very different mathematical object. While this result has applications in physics (e.g. string theory and Casimir effect), it should not be confused with the usual notion of summing natural numbers.
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